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On the Existence of Asymptotic-lp Structures in Banach Spaces
Published online by Cambridge University Press: 20 November 2018
Abstract
It is shown that if a Banach space is saturated with infinite dimensional subspaces in which all “special” $n$-tuples of vectors are equivalent with constants independent of
$n$-tuples and of
$n$, then the space contains asymptotic-
${{l}_{p}}$ subspaces for some
$1\,\le \,p\,\le \,\infty $. This extends a result by Figiel, Frankiewicz, Komorowski and Ryll-Nardzewski.
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- Copyright © Canadian Mathematical Society 2007
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